Direct and fast calculation of regularized cosmological power spectrum at two-loop order

We present a specific prescription for the calculation of cosmological power spectra, exploited here at two-loop order in perturbation theory, based on the multipoint propagator expansion. In this approach, density and velocity power spectra are constructed from the regularized expressions of the propagators that reproduce both the resummed behavior in the high-$k$ limit and the standard perturbation theory results at low $k$. With the help of $N$-body simulations, we particularly focus on the density field, and show that such a construction gives robust and accurate predictions for both the density power spectrum and the correlation function at percent level in the weakly nonlinear regime. We then present an algorithm that allows accelerated evaluations of all the required diagrams by reducing the computational tasks to one-dimensional integrals. This is achieved by means of precomputed kernel sets defined for appropriately chosen fiducial models. The computational time for two-loop results is then reduced from a few minutes, with the direct method, to a few seconds with the fast one. The robustness and applicability of this method are tested against the power spectrum cosmic emulator from which a wide variety of cosmological models can be explored. The Fortran program with which direct and fast calculations of density power spectra can be done, RegPT, is publicly released as part of this paper.